1. Field of the Invention
The invention relates to inertial guidance systems and, more particularly, to such systems for missiles which are launched vertically.
2. Description of the Prior Art
It has long been known in aerospace guidance to use gyroscopic sensing instruments mounted on a space stable or space-fixed platform within a frame and mounted to the frame by a two-degree-of-freedom gimbaling arrangement to assist in controlling the pitch and the yaw of the frame as it is propelled or guided through air, space or water. Hereinafter in this discussion, the term "frame" will be used to mean any structure which can be guided or propelled through air, water or space. A frame conventionally refers to an air frame such as a missile and, in some instances, to an airplane or rocket. The frame may have, and hereinafter in this discussion will be considered to always have, three dimensions which may, for convenience, be considered as extending in X axis, Y axis and Z axis directions. Rotation of the frame about the Y axis shall hereinafter be considered to be the pitch of the frame. Rotation of the frame about the Z axis shall hereinafter be considered the yaw of the frame. Rotation of the frame about the X axis shall hereinafter be considered the roll of the frame.
The X axis of the frame in most applications will constitute a longitudinal axis of the frame, such as a missile, airplane or rocket.
The platform mounted by gimbals within the frame may also be considered to extend in three dimensions. Hereinafter in this specification, the dimensions of the platform shall be considered to extend along its own A axis, B axis and C axis. The A, B and C axes are mutually orthogonal to each other. The pitch of the platform hereinafter shall be considered rotation about the B axis of the platform. The yaw of the platform shall hereinafter be considered the rotation about the C axis. Rotation of the platform about its A axis shall be considered its roll.
The frame is free to move. Its motion may be described by angular rates .omega..sub.x, .omega..sub.y, and .omega..sub.z of the respective axes X, Y and Z. The motion of the platform in inertial space may be expressed by the rotation .omega..sub.a, .omega..sub.b and .omega..sub.c about the A, B and C axes constituting the platform axes system. In order to maintain a true inertial reference and a true space stable inertial platform, it is necessary to control the three rotations .omega..sub.a, .omega..sub.b and .omega..sub.c.
It is known to use a two-gimbal system for mounting guidance platforms within missiles. In such a two-gimbal system, rotations about only two of the axes may be controlled. It is not possible to directly control the third axis rotation.
Consider, for example, a conventional two-gimbal system. Motion is only attainable through the gimbal axes which may not correspond to the orthogonal axes A, B and C of the platform system. Thus, the relationship of the outer gimbal relative to the frame may be described by the angle .alpha., and that of the inner gimbal relative to the frame outer gimbal by the angle .beta.. The angles .alpha. and .beta. are uniquely defined by the following matrix relationship between the platform and missile axis systems:
______________________________________ A cos.alpha.cos.beta. sin.alpha.cos.beta. -sin.beta. X (1) B = -sin.alpha. cos.alpha. 0 Y C cos.alpha.sin.beta. sin.alpha.sin.beta. cos.beta. Z ______________________________________
where A, B and C are components of a vector in the X, Y and Z axes system expressed in the A, B and C axes system. The angles .alpha. and .beta. are achieved by controlling the gimbal rates denoted .alpha. and .beta..
The rotational motion of the platform in inertial space can now be expressed in terms of the rotation of the missile .omega..sub.x, .omega..sub.y and .omega..sub.z and of the gimbal rotation .alpha. and .beta.:
______________________________________ .omega..sub.a = (cos.alpha.cos.beta.) .omega..sub.x + (sin.alpha.cos.beta.) .omega..sub.y - sin.beta.(.omega..sub.z +..alpha.) (2) .omega..sub.b = (-sin.alpha.) .omega..sub.x + (cos.alpha.) .omega..sub.y + ..beta. .omega..sub.c = (cos.alpha.sin.beta.) .omega..sub.x + (sin.alpha.cos.beta.) .omega..sub.y + cos.beta. (.omega..sub.z +..alpha.)
The rotation rates .omega..sub.x, .omega..sub.y and .omega..sub.z are disturbances to the platform. The gimbal rotation rates .alpha. and .beta. are available forcing inputs which may be used to stabilize the platform. In a conventional two-gimbal system, the gimbal rates .alpha. and .beta. are used to maintain respectively .omega..sub.c and .omega..sub.b at zero. Maintaining such rotations at zero will maintain the A axis in a fixed direction in space. The rotation .omega..sub.a, however, about the A axis cannot be controlled since .alpha. is already allocated as a driving function to control .omega..sub.c. Thus, the platform may unintentionally rotate or roll about its A axis and will not be a true inertial reference.
Attempts have been made to overcome this problem in guidance systems for missiles. In this regard, attention is directed to Stripling, U.S. Pat. No. 3,746,281. Stripling, representative of conventional, two-axes space-fixed platforms with pitch and yaw gimbals, suggests strapped-down, single-degree-of-freedom gyroscopically actuated roll control. Hereinafter in this specification, description of an element as being "strapped down" shall be used to mean that the element is fixed to the frame directly. Such strapped-down, single-degree-of-freedom, gyroscopically-actuated roll control, however, inherently defines a hybrid, and the platform used for guiding the frame is not a true inertial platform. It has long been sought to attain a true inertial platform for the guidance of frames, such as missiles, airplanes and rockets.